arXiv subjects

Yijia Dong

Publications and source records attributed to Yijia Dong.

2 recordsLinked to original sources

arXiv2026

Steady-State and Transient Heat Conduction Analysis Using a Polygonal Cell-Based Smoothed Finite Element Method

This paper presents a polygonal cell-based smoothed finite element method (CS-FEM) for two-dimensional steady-state and transient heat-conduction analysis. In the proposed formulation, Wachspress shape functions are employed to construct the temperature approximation over general polygonal elements, and the smoothed temperature gradient is evaluated through boundary integration over cell-based smoothing domains. The resulting formulation is implemented in ABAQUS through the user-defined element (UEL) interface, enabling heat-conduction analysis using polygonal meshes within a commercial finite element environment. Several numerical examples, including a linear patch test, steady-state benchmark problems, and transient heat-conduction problems with different boundary conditions, are investigated to verify the accuracy, convergence behavior, and robustness of the proposed method. The numerical results show good agreement with analytical or reference solutions. Compared with conventional FEM using triangular and quadrilateral elements, the proposed polygonal CS-FEM exhibits favorable accuracy and convergence performance, while providing greater flexibility in mesh generation for complex geometries. The proposed framework therefore offers an accurate and robust numerical approach for steady-state and transient heat-conduction analysis.

math.NT↗

arXiv2026

Nonlinear Geotechnical Analysis Using a Polygonal Cell-Based Smoothed Finite Element Framework

Nonlinear geotechnical analysis often involves complex geometries, staged construction, local failure, and mesh-dependent stress and plastic strain responses. This study develops a polygonal cell-based smoothed finite element method (CS-FEM) for nonlinear geotechnical analysis and implements it in ABAQUS through the user element subroutine. The proposed method combines Wachspress interpolation with cell-based strain smoothing, in which the smoothed strain--displacement matrix is evaluated by boundary integration over polygonal smoothing subcells. This formulation avoids direct calculation of shape-function derivatives inside polygonal elements and enables standard polygonal meshes and hybrid quadtree meshes with hanging nodes to be handled in a unified framework. Nonlinear geomaterial behavior is incorporated through incremental elasto-plastic constitutive updates, including the Mohr--Coulomb model and the Duncan--Chang model. Several benchmark and engineering examples, including a perforated plate, strip footing, core rockfill dam, tunnel excavation, and slope stability problems, are presented for verification. The results show that the proposed method accurately predicts displacement, stress, plastic strain, bearing capacity, and factor of safety, while providing improved mesh flexibility and computational efficiency for nonlinear geotechnical analysis.

math.NA↗